Question:
Solution:
The intercept form of a quadratic equation (a parabola) is given by the following formula:
[tex]y\text{ = }a(x-p)(x-q)[/tex]
where p and q are the x-coordinate of the x-intercept of the parabola. In this case, notice that:
p = 2 and q = 4
then we have the preliminary equation:
EQUATION 1:
[tex]y\text{ = }a(x-2)(x-4)[/tex]
now, to find a, replace the point (x,y) = (3,4) in the previous equation. so that, we obtain:
[tex]4\text{ = }a(3-2)(3-4)[/tex]
this is equivalent to:
[tex]4\text{ = }a(1)(-1)\text{ = -a}[/tex]
thus
[tex]a\text{ = -4}[/tex]
then, replacing a = -4 into the EQUATION 1, we get:
[tex]y\text{ = -4}(x-2)(x-4)[/tex]
Then, we can conclude that the equation of the given parabola in the intercept form is:
[tex]y\text{ = -4}(x-2)(x-4)[/tex]
